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Triangular NURBS and their dynamic generalizations

Hong Qin, Demetri Terzopoulos
1997 Computer Aided Geometric Design  
Triangular B-splines are a new tool for modeling a broad class of objects defined over arbitrary, nonrectangular domains.  ...  They provide an elegant and unified representation scheme for all piecewise continuous polynomial surfaces over planar triangulations.  ...  Acknowledgments We would like to thank Professor Hans-Peter Seidel of Universit~it Erlangen for kindly making available the software for triangular B-spline surfaces that he developed with Mr.  ... 
doi:10.1016/s0167-8396(96)00062-3 fatcat:5pyhbzjurzh2hggwdeaai4dro4

Dynamic manipulation of triangular B-splines

Hong Qin, Demetri Terzopoulos
1995 Proceedings of the third ACM symposium on Solid modeling and applications - SMA '95  
As an alternative, we develop a new model based on the elegant triangular B-spline geometry and principles of physical dynamics.  ...  They are useful for modeling a broad class of complex objects defined over arbitrary, nonrectangular domains.  ...  Acknowledgments We are grateful to Professor Hans-Peter Seidel for kindly making available the software for triangular B-spline surfaces that he developed with Philip Fong.  ... 
doi:10.1145/218013.218084 dblp:conf/sma/QinT95 fatcat:aadkvyhr7rf2zhnzruekddjqny

Page 6644 of Mathematical Reviews Vol. , Issue 94k [page]

1994 Mathematical Reviews  
Franz Peherstorfer (A-LINZ; Linz) 94k:65017 65D07 41A15 Fong, Philip (3-WTRL-C; Waterloo, ON); Seidel, Hans-Peter (D-ERL-GD; Erlangen) An implementation of triangular B-spline surfaces over arbitrary triangulations  ...  Fong “Shape control for B-splines over arbitrary triangulations”, Master’s Thesis, Univ. Waterloo, Waterloo, ON, 1992; per bibl.]. 65 NUMERICAL ANALYSIS 6644 Given an arbitrary triangulation T of R?  ... 

Splines and geometric modeling [chapter]

Chandrajit Bajaj
2004 Handbook of Discrete and Computational Geometry, Second Edition  
The surface scheme is an approximation scheme based on blending functions and control points and allows the modeling of C k,1 continuous piecewise polynomial surfaces of degree k over arbitrary triangulations  ...  Splines over arbitrary triangulations of the parameter plane were rst considered by Dahmen and Michelli DM82 and H ollig Hol82 .  ... 
doi:10.1201/9781420035315.ch53 fatcat:e7evq2b77ba5lj3vxlcxwxxzda

A C 1 Globally Interpolatory Spline of Arbitrary Topology [chapter]

Ying He, Miao Jin, Xianfeng Gu, Hong Qin
2005 Lecture Notes in Computer Science  
Starting from the Powell-Sabin spline as a building block, we integrate the concepts of global parametrization, affine atlas, and splines defined over local, open domains to arrive at an elegant, easy-to-use  ...  The proposed global spline scheme enables the rapid surface reconstruction and facilitates the shape editing and analysis functionality.  ...  Figure 3 illustrates an example of Powell-Sabin spline surface over a planar triangulated domain. Note that, their basis functions B j i (u) vanish outside the molecule M i (see Figure 3 (e-h)).  ... 
doi:10.1007/11567646_25 fatcat:vbzdt43br5c7zcyeglnidihaly

Spline Thin-Shell Simulation of Manifold Surfaces [chapter]

Kexiang Wang, Ying He, Xiaohu Guo, Hong Qin
2006 Lecture Notes in Computer Science  
The deformation is represented as a linear combination of triangular B-splines over shell surfaces, then the dynamics of thin-shell simulation is computed through the minimization of Kirchhoff-Love energy  ...  In particular, we systematically extend the triangular B-spline FEM from planar domains to manifold domains.  ...  For examples, manifold triangular B-splines are piecewise polynomial defined on the manifold domain of arbitrary triangulation.  ... 
doi:10.1007/11784203_53 fatcat:odauljhibzfi5g7qxgvi6m6qxy

Incorporating Rigid Structures in Non-rigid Registration Using Triangular B-Splines [chapter]

Kexiang Wang, Ying He, Hong Qin
2005 Lecture Notes in Computer Science  
features (C 0 continuity) along the interface between deformable regions and rigid structures, because of the unique advantages offered by triangular B-splines, such as flexible triangular domain, local  ...  In this paper, we introduce a novel registration technique that models local rigidity of pre-identified rigid structures as well as global non-rigidity in the transformation field using triangular B-splines  ...  Pfeifle and Seidel [19] presented an efficient algorithm to evaluate quadratic triangular B-splines and Franssen et al. [20] extended it to triangular B-splines of arbitrary degree.  ... 
doi:10.1007/11567646_20 fatcat:lbcoo4ezbzeilcft567zjzgb7i

Multilevel refinable triangular PSP-splines (Tri-PSPS)

Qingde Li, Jie Tian
2015 Computers and Mathematics with Applications  
of the PSPS can be directly built from an arbitrary set of polygons that partitions a giving parametric domain.  ...  Secondly, Tri-PSPS are an additive triangular spline technique, where the spline function built from a given triangle can be replaced with a set of refined spline functions built on a set of smaller triangles  ...  The function built in this way for an arbitrary polygon is independent of the ways that the given polygon is triangulated.  ... 
doi:10.1016/j.camwa.2015.07.017 fatcat:ppgs52ib4ngjnioaek5qoc4oze

Surface reconstruction using bivariate simplex splines on Delaunay configurations

Juan Cao, Xin Li, Guozhao Wang, Hong Qin
2009 Computers & graphics  
Unlike existing surface reconstruction methods based on triangular B-splines (or DMS splines), in which auxiliary knots must be explicitly added in advance to form a knot sequence for construction of each  ...  In this paper, we develop a novel shape modeling framework to reconstruct a closed surface of arbitrary topology based on this new spline scheme.  ...  This work is partially supported by NSF IIS-0710819, NSF IIS-0326338, Louisiana Board of Regents PFund: NSF(2009)-PFUND-133, and the Natural Science Foundation of China 60773179.  ... 
doi:10.1016/j.cag.2009.03.013 fatcat:erkdsfmsn5d6zcygwex4mcy6lm

Construction of multiresolution triangular B-spline surfaces using hexagonal filters

A. Dreger, M.H. Gross, J. Schlegel
2000 The Visual Computer  
We present multiresolution B-spline surfaces of arbitrary order defined over triangular domains.  ...  The scheme works for splines of any order where the fundamental building blocks of the surface are hierarchies of triangular B-spline scaling functions and wavelets spanning the complement spaces between  ...  triangular B-spline surfaces of arbitrary polynomial order.  ... 
doi:10.1007/s003710000073 fatcat:iecsy2xskvhxjdvgvlsmr7rrjy

Manifold splines

Xianfeng Gu, Ying He, Hong Qin
2005 Proceedings of the 2005 ACM symposium on Solid and physical modeling - SPM '05  
We choose triangular B-splines mainly because of its generality and many of its attractive properties.  ...  Based on our theoretical breakthrough, we also develop a set of practical algorithms to generalize triangular B-spline surfaces from planar domains to manifold domains.  ...  over arbitrary planar triangulations, and they generalize tensor-product B-splines.  ... 
doi:10.1145/1060244.1060249 dblp:conf/sma/GuHQ05 fatcat:inyekbp2gvf3tlerj6qoiv236i

Manifold splines

Xianfeng Gu, Ying He, Hong Qin
2006 Graphical Models  
We choose triangular B-splines mainly because of its generality and many of its attractive properties.  ...  Based on our theoretical breakthrough, we also develop a set of practical algorithms to generalize triangular B-spline surfaces from planar domains to manifold domains.  ...  over arbitrary planar triangulations, and they generalize tensor-product B-splines.  ... 
doi:10.1016/j.gmod.2006.03.004 fatcat:vlkc4cify5ffjf7dflyxy36cwa

Fitting Surface of Free Form Objects using Optimized NURBS Patches Network with Evolutionary Strategies (mu + lambda) - ES

J. W. Branch, F. Prieto, P. Boulanger
2007 Procedings of the British Machine Vision Conference 2007  
We propose an algorithm to produce a 3-D CAD model from a set of range data, based on non-uniform rational B-splines (NURBS) surface fitting technique.  ...  The quadrilateral obtained mesh is regularized by means of the use of geodesic curves and B-splines to obtain a new adequate grid on which to draw NURBS surfaces.  ...  The formulation of C 1 continuity presented in this paper can be generalized, because it can be used to approximate regular and irregular neighborhoods which present model processes regardless of partitioning  ... 
doi:10.5244/c.21.99 dblp:conf/bmvc/BranchPB07 fatcat:nxb4irsoabainbo2jfrz6v22mm

Supporting Automated Pen and Ink Style Surface Illustration with B-Spline Models

James E. Mower
2011 Cartography and Geographic Information Science  
In B, surface masking resolves the intersection problem. Figure 7 . 7 An arbitrary grid rendered as a B-spline surface with non-emissive gray shading.  ...  Figure 7 shows an example of a rendered B-spline surface shaded with a non-emissive color.  ... 
doi:10.1559/15230406382161 fatcat:lnjrphw6czdzjpphc33h2qpc7m

Efficient evaluation of triangular B-spline surfaces

Michael Franssen, Remco C. Veltkamp, Wieger Wesselink
2000 Computer Aided Geometric Design  
Evaluation routines are essential for any application that uses triangular B-splines. This paper describes an algorithm to efficiently evaluate triangular B-splines.  ...  The novelty of the algorithm is its generality: there is no restriction on the degree of the B-spline or on the dimension of the domain.  ...  Definition of triangular B-splines Definition 2.6 [Triangular B-splines] A triangular B-splines is a piecewise polynomial function defined over an arbitrary polygonal domain in rn?  ... 
doi:10.1016/s0167-8396(00)00030-3 fatcat:lfhuzyv4cfd5xoyeqyfc3ktwwm
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